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What is the ILD (Influence Line Diagram) of a three hinged Arch of Span 'L' and rise 'h' due to horizontal thrust 'H'

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DSSSB AE Civil 26 Sept 2021 Official Paper
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  1. Triangle with its maximum ordinate at center equals to \(\frac{L}{24h}\)
  2. Square with its ordinate equals to \(\frac{L}{24h}\)
  3. Square with its ordinate equals to \(\frac{L}{2h}\)
  4. Triangle with its maximum ordinate at center equals to \(\frac{L}{4h}\)

Answer (Detailed Solution Below)

Option 4 : Triangle with its maximum ordinate at center equals to \(\frac{L}{4h}\)
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Detailed Solution

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Concept:

For a 3 hinged arch due to horizontal thrust 'H':

F1 A.M Madhu 09.07.20 D13

ILD for beam moment in 3 hinged arch:

F1 A.M Madhu 09.07.20 D14

Bending moment in an arch is due to the combined action of beam moment & moment due to horizontal thrust. ILD for BM:

F1 A.M Madhu 09.07.20 D15

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More 3 Hinged Questions

Q1.A parabolic 3 hinged arch (AB) carries a u.d.l. of 30 kN/m on the left half of the span. It has a span of 16 m and a central rise of 3 m. What is the resultant thrust at 'A' (left hand end)?
Q2.A three hinged arch carries a load as shown. The horizontal thrust is :
Q3.If ‘L’ is the span of a three hinged arch, ‘h’ is the rise and ‘W’ is the u.d.l per unit length over the entire span, the horizontal reaction at each support is given by:
Q4.What is the ILD (Influence Line Diagram) of a three hinged Arch of Span 'L' and rise 'h' due to horizontal thrust 'H'
Q5.For a three-hinged parabolic arch, what will be the ratio L/R to satisfy H= W?
Q6.A parabolic three hinged arch ABC is supporting Uniformly Distributed Load of 500 N/m over its entire span of 100 m. The centre point ‘B’ is vertically 25 m high from supports A and C. The reactions shall be ______.
Q7.A three-hinged parabolic arch has a span of 30 m and the central rise is 5 m. It is subjected to a point load of 40 kN at a distance of 20 m from the right hinge. Calculate the vertical reaction component at its left support.
Q8.A three-hinged parabolic arch of span 20 m and rise 4 m carries a concentrated load of 150 kN at 4 m from left support 'A'. Calculate the vertical reaction and the horizontal thrust, respectively, at support 'A'.
Q9.A three hinged arch is

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Q1.A three-hinged arch is statically 
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Q4.A parabolic 3 hinged arch (AB) carries a u.d.l. of 30 kN/m on the left half of the span. It has a span of 16 m and a central rise of 3 m. What is the resultant thrust at 'A' (left hand end)?
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